PNG (8 bit with basic alpha)
PNG (24-32 bit with full alpha)
Hopefully you have a vector (AI, EPS PDF) or at least a layered PSD or TIFF version of your logo, making it straight forward to re-save/export the image as a PNG with full transparency using the 'Save As' options or equivalent in your image editor.
If not you'll need to convert a 'flat' version of your logo by removing the background manually, ensuring you have a high resolution (at least as big as the 'Large' version required by the mobile application) as a starting point.